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On the distribution of square-full integers

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Abstract

Let S(x) be the number of square-full integers not exceeding x and let \(\Delta (x)\) be the error term in the asymptotic formula for S(x). Under the Riemann hypothesis, we get that \(\Delta (x)\ll x^{\frac{328}{2333}}\), which improves the exponent \(\frac{121}{860}\) obtained by Liu [6].

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Acknowledgements

The author is very grateful to the reviewers for many valuable suggestions and comments. Many thanks to Timothy Scott Trudgian for many useful discussions and valuable suggestions and the UNSW Study Abroad Research Practicum Program. This work is supported by a scholarship from the China Scholarship Council.

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Authors and Affiliations

  1. School of Mathematics and Statistics, Qilu University of Technology (Shandong Academy of Sciences), Jinan, 250353, Shandong, China

    Dan Wang

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  1. Dan Wang
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Correspondence to Dan Wang.

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Communicated by C. S. Rajan.

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Wang, D. On the distribution of square-full integers. Indian J Pure Appl Math 53, 627–634 (2022). https://doi.org/10.1007/s13226-021-00154-0

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  • DOI: https://doi.org/10.1007/s13226-021-00154-0

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